[37] | 1 | //---------------------------------------------------------------------- |
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| 2 | // File: kd_util.cpp |
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| 3 | // Programmer: Sunil Arya and David Mount |
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| 4 | // Description: Common utilities for kd-trees |
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| 5 | // Last modified: 01/04/05 (Version 1.0) |
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| 6 | //---------------------------------------------------------------------- |
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| 7 | // Copyright (c) 1997-2005 University of Maryland and Sunil Arya and |
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| 8 | // David Mount. All Rights Reserved. |
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| 9 | // |
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| 10 | // This software and related documentation is part of the Approximate |
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| 11 | // Nearest Neighbor Library (ANN). This software is provided under |
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| 12 | // the provisions of the Lesser GNU Public License (LGPL). See the |
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| 13 | // file ../ReadMe.txt for further information. |
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| 14 | // |
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| 15 | // The University of Maryland (U.M.) and the authors make no |
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| 16 | // representations about the suitability or fitness of this software for |
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| 17 | // any purpose. It is provided "as is" without express or implied |
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| 18 | // warranty. |
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| 19 | //---------------------------------------------------------------------- |
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| 20 | // History: |
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| 21 | // Revision 0.1 03/04/98 |
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| 22 | // Initial release |
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| 23 | //---------------------------------------------------------------------- |
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| 24 | |
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| 25 | #include "kd_util.h" // kd-utility declarations |
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| 26 | |
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| 27 | #include <ANN/ANNperf.h> // performance evaluation |
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| 28 | |
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| 29 | //---------------------------------------------------------------------- |
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| 30 | // The following routines are utility functions for manipulating |
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| 31 | // points sets, used in determining splitting planes for kd-tree |
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| 32 | // construction. |
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| 33 | //---------------------------------------------------------------------- |
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| 34 | |
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| 35 | //---------------------------------------------------------------------- |
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| 36 | // NOTE: Virtually all point indexing is done through an index (i.e. |
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| 37 | // permutation) array pidx. Consequently, a reference to the d-th |
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| 38 | // coordinate of the i-th point is pa[pidx[i]][d]. The macro PA(i,d) |
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| 39 | // is a shorthand for this. |
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| 40 | //---------------------------------------------------------------------- |
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| 41 | // standard 2-d indirect indexing |
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| 42 | #define PA(i,d) (pa[pidx[(i)]][(d)]) |
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| 43 | // accessing a single point |
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| 44 | #define PP(i) (pa[pidx[(i)]]) |
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| 45 | |
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| 46 | //---------------------------------------------------------------------- |
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| 47 | // annAspectRatio |
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| 48 | // Compute the aspect ratio (ratio of longest to shortest side) |
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| 49 | // of a rectangle. |
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| 50 | //---------------------------------------------------------------------- |
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| 51 | |
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| 52 | double annAspectRatio( |
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| 53 | int dim, // dimension |
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| 54 | const ANNorthRect &bnd_box) // bounding cube |
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| 55 | { |
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| 56 | ANNcoord length = bnd_box.hi[0] - bnd_box.lo[0]; |
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| 57 | ANNcoord min_length = length; // min side length |
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| 58 | ANNcoord max_length = length; // max side length |
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| 59 | for (int d = 0; d < dim; d++) { |
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| 60 | length = bnd_box.hi[d] - bnd_box.lo[d]; |
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| 61 | if (length < min_length) min_length = length; |
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| 62 | if (length > max_length) max_length = length; |
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| 63 | } |
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| 64 | return max_length/min_length; |
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| 65 | } |
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| 66 | |
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| 67 | //---------------------------------------------------------------------- |
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| 68 | // annEnclRect, annEnclCube |
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| 69 | // These utilities compute the smallest rectangle and cube enclosing |
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| 70 | // a set of points, respectively. |
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| 71 | //---------------------------------------------------------------------- |
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| 72 | |
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| 73 | void annEnclRect( |
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| 74 | ANNpointArray pa, // point array |
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| 75 | ANNidxArray pidx, // point indices |
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| 76 | int n, // number of points |
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| 77 | int dim, // dimension |
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| 78 | ANNorthRect &bnds) // bounding cube (returned) |
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| 79 | { |
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| 80 | for (int d = 0; d < dim; d++) { // find smallest enclosing rectangle |
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| 81 | ANNcoord lo_bnd = PA(0,d); // lower bound on dimension d |
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| 82 | ANNcoord hi_bnd = PA(0,d); // upper bound on dimension d |
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| 83 | for (int i = 0; i < n; i++) { |
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| 84 | if (PA(i,d) < lo_bnd) lo_bnd = PA(i,d); |
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| 85 | else if (PA(i,d) > hi_bnd) hi_bnd = PA(i,d); |
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| 86 | } |
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| 87 | bnds.lo[d] = lo_bnd; |
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| 88 | bnds.hi[d] = hi_bnd; |
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| 89 | } |
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| 90 | } |
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| 91 | |
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| 92 | void annEnclCube( // compute smallest enclosing cube |
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| 93 | ANNpointArray pa, // point array |
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| 94 | ANNidxArray pidx, // point indices |
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| 95 | int n, // number of points |
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| 96 | int dim, // dimension |
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| 97 | ANNorthRect &bnds) // bounding cube (returned) |
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| 98 | { |
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| 99 | int d; |
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| 100 | // compute smallest enclosing rect |
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| 101 | annEnclRect(pa, pidx, n, dim, bnds); |
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| 102 | |
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| 103 | ANNcoord max_len = 0; // max length of any side |
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| 104 | for (d = 0; d < dim; d++) { // determine max side length |
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| 105 | ANNcoord len = bnds.hi[d] - bnds.lo[d]; |
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| 106 | if (len > max_len) { // update max_len if longest |
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| 107 | max_len = len; |
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| 108 | } |
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| 109 | } |
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| 110 | for (d = 0; d < dim; d++) { // grow sides to match max |
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| 111 | ANNcoord len = bnds.hi[d] - bnds.lo[d]; |
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| 112 | ANNcoord half_diff = (max_len - len) / 2; |
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| 113 | bnds.lo[d] -= half_diff; |
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| 114 | bnds.hi[d] += half_diff; |
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| 115 | } |
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| 116 | } |
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| 117 | |
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| 118 | //---------------------------------------------------------------------- |
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| 119 | // annBoxDistance - utility routine which computes distance from point to |
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| 120 | // box (Note: most distances to boxes are computed using incremental |
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| 121 | // distance updates, not this function.) |
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| 122 | //---------------------------------------------------------------------- |
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| 123 | |
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| 124 | ANNdist annBoxDistance( // compute distance from point to box |
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| 125 | const ANNpoint q, // the point |
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| 126 | const ANNpoint lo, // low point of box |
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| 127 | const ANNpoint hi, // high point of box |
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| 128 | int dim) // dimension of space |
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| 129 | { |
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| 130 | register ANNdist dist = 0.0; // sum of squared distances |
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| 131 | register ANNdist t; |
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| 132 | |
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| 133 | for (register int d = 0; d < dim; d++) { |
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| 134 | if (q[d] < lo[d]) { // q is left of box |
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| 135 | t = ANNdist(lo[d]) - ANNdist(q[d]); |
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| 136 | dist = ANN_SUM(dist, ANN_POW(t)); |
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| 137 | } |
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| 138 | else if (q[d] > hi[d]) { // q is right of box |
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| 139 | t = ANNdist(q[d]) - ANNdist(hi[d]); |
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| 140 | dist = ANN_SUM(dist, ANN_POW(t)); |
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| 141 | } |
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| 142 | } |
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| 143 | ANN_FLOP(4*dim) // increment floating op count |
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| 144 | |
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| 145 | return dist; |
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| 146 | } |
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| 147 | |
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| 148 | //---------------------------------------------------------------------- |
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| 149 | // annSpread - find spread along given dimension |
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| 150 | // annMinMax - find min and max coordinates along given dimension |
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| 151 | // annMaxSpread - find dimension of max spread |
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| 152 | //---------------------------------------------------------------------- |
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| 153 | |
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| 154 | ANNcoord annSpread( // compute point spread along dimension |
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| 155 | ANNpointArray pa, // point array |
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| 156 | ANNidxArray pidx, // point indices |
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| 157 | int n, // number of points |
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| 158 | int d) // dimension to check |
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| 159 | { |
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| 160 | ANNcoord min = PA(0,d); // compute max and min coords |
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| 161 | ANNcoord max = PA(0,d); |
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| 162 | for (int i = 1; i < n; i++) { |
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| 163 | ANNcoord c = PA(i,d); |
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| 164 | if (c < min) min = c; |
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| 165 | else if (c > max) max = c; |
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| 166 | } |
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| 167 | return (max - min); // total spread is difference |
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| 168 | } |
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| 169 | |
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| 170 | void annMinMax( // compute min and max coordinates along dim |
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| 171 | ANNpointArray pa, // point array |
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| 172 | ANNidxArray pidx, // point indices |
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| 173 | int n, // number of points |
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| 174 | int d, // dimension to check |
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| 175 | ANNcoord &min, // minimum value (returned) |
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| 176 | ANNcoord &max) // maximum value (returned) |
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| 177 | { |
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| 178 | min = PA(0,d); // compute max and min coords |
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| 179 | max = PA(0,d); |
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| 180 | for (int i = 1; i < n; i++) { |
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| 181 | ANNcoord c = PA(i,d); |
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| 182 | if (c < min) min = c; |
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| 183 | else if (c > max) max = c; |
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| 184 | } |
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| 185 | } |
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| 186 | |
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| 187 | int annMaxSpread( // compute dimension of max spread |
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| 188 | ANNpointArray pa, // point array |
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| 189 | ANNidxArray pidx, // point indices |
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| 190 | int n, // number of points |
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| 191 | int dim) // dimension of space |
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| 192 | { |
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| 193 | int max_dim = 0; // dimension of max spread |
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| 194 | ANNcoord max_spr = 0; // amount of max spread |
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| 195 | |
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| 196 | if (n == 0) return max_dim; // no points, who cares? |
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| 197 | |
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| 198 | for (int d = 0; d < dim; d++) { // compute spread along each dim |
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| 199 | ANNcoord spr = annSpread(pa, pidx, n, d); |
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| 200 | if (spr > max_spr) { // bigger than current max |
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| 201 | max_spr = spr; |
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| 202 | max_dim = d; |
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| 203 | } |
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| 204 | } |
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| 205 | return max_dim; |
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| 206 | } |
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| 207 | |
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| 208 | //---------------------------------------------------------------------- |
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| 209 | // annMedianSplit - split point array about its median |
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| 210 | // Splits a subarray of points pa[0..n] about an element of given |
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| 211 | // rank (median: n_lo = n/2) with respect to dimension d. It places |
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| 212 | // the element of rank n_lo-1 correctly (because our splitting rule |
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| 213 | // takes the mean of these two). On exit, the array is permuted so |
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| 214 | // that: |
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| 215 | // |
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| 216 | // pa[0..n_lo-2][d] <= pa[n_lo-1][d] <= pa[n_lo][d] <= pa[n_lo+1..n-1][d]. |
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| 217 | // |
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| 218 | // The mean of pa[n_lo-1][d] and pa[n_lo][d] is returned as the |
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| 219 | // splitting value. |
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| 220 | // |
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| 221 | // All indexing is done indirectly through the index array pidx. |
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| 222 | // |
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| 223 | // This function uses the well known selection algorithm due to |
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| 224 | // C.A.R. Hoare. |
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| 225 | //---------------------------------------------------------------------- |
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| 226 | |
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| 227 | // swap two points in pa array |
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| 228 | #define PASWAP(a,b) { int tmp = pidx[a]; pidx[a] = pidx[b]; pidx[b] = tmp; } |
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| 229 | |
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| 230 | void annMedianSplit( |
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| 231 | ANNpointArray pa, // points to split |
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| 232 | ANNidxArray pidx, // point indices |
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| 233 | int n, // number of points |
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| 234 | int d, // dimension along which to split |
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| 235 | ANNcoord &cv, // cutting value |
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| 236 | int n_lo) // split into n_lo and n-n_lo |
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| 237 | { |
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| 238 | int l = 0; // left end of current subarray |
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| 239 | int r = n-1; // right end of current subarray |
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| 240 | while (l < r) { |
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| 241 | register int i = (r+l)/2; // select middle as pivot |
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| 242 | register int k; |
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| 243 | |
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| 244 | if (PA(i,d) > PA(r,d)) // make sure last > pivot |
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| 245 | PASWAP(i,r) |
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| 246 | PASWAP(l,i); // move pivot to first position |
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| 247 | |
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| 248 | ANNcoord c = PA(l,d); // pivot value |
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| 249 | i = l; |
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| 250 | k = r; |
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| 251 | for(;;) { // pivot about c |
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| 252 | while (PA(++i,d) < c) ; |
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| 253 | while (PA(--k,d) > c) ; |
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| 254 | if (i < k) PASWAP(i,k) else break; |
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| 255 | } |
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| 256 | PASWAP(l,k); // pivot winds up in location k |
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| 257 | |
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| 258 | if (k > n_lo) r = k-1; // recurse on proper subarray |
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| 259 | else if (k < n_lo) l = k+1; |
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| 260 | else break; // got the median exactly |
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| 261 | } |
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| 262 | if (n_lo > 0) { // search for next smaller item |
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| 263 | ANNcoord c = PA(0,d); // candidate for max |
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| 264 | int k = 0; // candidate's index |
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| 265 | for (int i = 1; i < n_lo; i++) { |
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| 266 | if (PA(i,d) > c) { |
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| 267 | c = PA(i,d); |
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| 268 | k = i; |
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| 269 | } |
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| 270 | } |
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| 271 | PASWAP(n_lo-1, k); // max among pa[0..n_lo-1] to pa[n_lo-1] |
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| 272 | } |
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| 273 | // cut value is midpoint value |
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| 274 | cv = (PA(n_lo-1,d) + PA(n_lo,d))/2.0; |
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| 275 | } |
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| 276 | |
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| 277 | //---------------------------------------------------------------------- |
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| 278 | // annPlaneSplit - split point array about a cutting plane |
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| 279 | // Split the points in an array about a given plane along a |
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| 280 | // given cutting dimension. On exit, br1 and br2 are set so |
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| 281 | // that: |
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| 282 | // |
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| 283 | // pa[ 0 ..br1-1] < cv |
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| 284 | // pa[br1..br2-1] == cv |
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| 285 | // pa[br2.. n -1] > cv |
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| 286 | // |
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| 287 | // All indexing is done indirectly through the index array pidx. |
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| 288 | // |
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| 289 | //---------------------------------------------------------------------- |
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| 290 | |
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| 291 | void annPlaneSplit( // split points by a plane |
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| 292 | ANNpointArray pa, // points to split |
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| 293 | ANNidxArray pidx, // point indices |
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| 294 | int n, // number of points |
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| 295 | int d, // dimension along which to split |
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| 296 | ANNcoord cv, // cutting value |
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| 297 | int &br1, // first break (values < cv) |
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| 298 | int &br2) // second break (values == cv) |
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| 299 | { |
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| 300 | int l = 0; |
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| 301 | int r = n-1; |
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| 302 | for(;;) { // partition pa[0..n-1] about cv |
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| 303 | while (l < n && PA(l,d) < cv) l++; |
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| 304 | while (r >= 0 && PA(r,d) >= cv) r--; |
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| 305 | if (l > r) break; |
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| 306 | PASWAP(l,r); |
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| 307 | l++; r--; |
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| 308 | } |
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| 309 | br1 = l; // now: pa[0..br1-1] < cv <= pa[br1..n-1] |
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| 310 | r = n-1; |
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| 311 | for(;;) { // partition pa[br1..n-1] about cv |
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| 312 | while (l < n && PA(l,d) <= cv) l++; |
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| 313 | while (r >= br1 && PA(r,d) > cv) r--; |
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| 314 | if (l > r) break; |
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| 315 | PASWAP(l,r); |
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| 316 | l++; r--; |
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| 317 | } |
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| 318 | br2 = l; // now: pa[br1..br2-1] == cv < pa[br2..n-1] |
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| 319 | } |
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| 320 | |
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| 321 | |
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| 322 | //---------------------------------------------------------------------- |
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| 323 | // annBoxSplit - split point array about a orthogonal rectangle |
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| 324 | // Split the points in an array about a given orthogonal |
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| 325 | // rectangle. On exit, n_in is set to the number of points |
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| 326 | // that are inside (or on the boundary of) the rectangle. |
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| 327 | // |
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| 328 | // All indexing is done indirectly through the index array pidx. |
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| 329 | // |
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| 330 | //---------------------------------------------------------------------- |
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| 331 | |
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| 332 | void annBoxSplit( // split points by a box |
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| 333 | ANNpointArray pa, // points to split |
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| 334 | ANNidxArray pidx, // point indices |
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| 335 | int n, // number of points |
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| 336 | int dim, // dimension of space |
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| 337 | ANNorthRect &box, // the box |
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| 338 | int &n_in) // number of points inside (returned) |
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| 339 | { |
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| 340 | int l = 0; |
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| 341 | int r = n-1; |
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| 342 | for(;;) { // partition pa[0..n-1] about box |
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| 343 | while (l < n && box.inside(dim, PP(l))) l++; |
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| 344 | while (r >= 0 && !box.inside(dim, PP(r))) r--; |
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| 345 | if (l > r) break; |
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| 346 | PASWAP(l,r); |
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| 347 | l++; r--; |
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| 348 | } |
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| 349 | n_in = l; // now: pa[0..n_in-1] inside and rest outside |
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| 350 | } |
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| 351 | |
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| 352 | //---------------------------------------------------------------------- |
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| 353 | // annSplitBalance - compute balance factor for a given plane split |
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| 354 | // Balance factor is defined as the number of points lying |
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| 355 | // below the splitting value minus n/2 (median). Thus, a |
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| 356 | // median split has balance 0, left of this is negative and |
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| 357 | // right of this is positive. (The points are unchanged.) |
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| 358 | //---------------------------------------------------------------------- |
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| 359 | |
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| 360 | int annSplitBalance( // determine balance factor of a split |
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| 361 | ANNpointArray pa, // points to split |
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| 362 | ANNidxArray pidx, // point indices |
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| 363 | int n, // number of points |
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| 364 | int d, // dimension along which to split |
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| 365 | ANNcoord cv) // cutting value |
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| 366 | { |
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| 367 | int n_lo = 0; |
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| 368 | for(int i = 0; i < n; i++) { // count number less than cv |
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| 369 | if (PA(i,d) < cv) n_lo++; |
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| 370 | } |
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| 371 | return n_lo - n/2; |
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| 372 | } |
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| 373 | |
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| 374 | //---------------------------------------------------------------------- |
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| 375 | // annBox2Bnds - convert bounding box to list of bounds |
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| 376 | // Given two boxes, an inner box enclosed within a bounding |
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| 377 | // box, this routine determines all the sides for which the |
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| 378 | // inner box is strictly contained with the bounding box, |
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| 379 | // and adds an appropriate entry to a list of bounds. Then |
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| 380 | // we allocate storage for the final list of bounds, and return |
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| 381 | // the resulting list and its size. |
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| 382 | //---------------------------------------------------------------------- |
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| 383 | |
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| 384 | void annBox2Bnds( // convert inner box to bounds |
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| 385 | const ANNorthRect &inner_box, // inner box |
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| 386 | const ANNorthRect &bnd_box, // enclosing box |
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| 387 | int dim, // dimension of space |
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| 388 | int &n_bnds, // number of bounds (returned) |
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| 389 | ANNorthHSArray &bnds) // bounds array (returned) |
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| 390 | { |
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| 391 | int i; |
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| 392 | n_bnds = 0; // count number of bounds |
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| 393 | for (i = 0; i < dim; i++) { |
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| 394 | if (inner_box.lo[i] > bnd_box.lo[i]) // low bound is inside |
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| 395 | n_bnds++; |
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| 396 | if (inner_box.hi[i] < bnd_box.hi[i]) // high bound is inside |
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| 397 | n_bnds++; |
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| 398 | } |
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| 399 | |
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| 400 | bnds = new ANNorthHalfSpace[n_bnds]; // allocate appropriate size |
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| 401 | |
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| 402 | int j = 0; |
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| 403 | for (i = 0; i < dim; i++) { // fill the array |
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| 404 | if (inner_box.lo[i] > bnd_box.lo[i]) { |
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| 405 | bnds[j].cd = i; |
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| 406 | bnds[j].cv = inner_box.lo[i]; |
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| 407 | bnds[j].sd = +1; |
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| 408 | j++; |
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| 409 | } |
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| 410 | if (inner_box.hi[i] < bnd_box.hi[i]) { |
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| 411 | bnds[j].cd = i; |
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| 412 | bnds[j].cv = inner_box.hi[i]; |
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| 413 | bnds[j].sd = -1; |
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| 414 | j++; |
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| 415 | } |
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| 416 | } |
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| 417 | } |
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| 418 | |
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| 419 | //---------------------------------------------------------------------- |
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| 420 | // annBnds2Box - convert list of bounds to bounding box |
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| 421 | // Given an enclosing box and a list of bounds, this routine |
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| 422 | // computes the corresponding inner box. It is assumed that |
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| 423 | // the box points have been allocated already. |
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| 424 | //---------------------------------------------------------------------- |
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| 425 | |
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| 426 | void annBnds2Box( |
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| 427 | const ANNorthRect &bnd_box, // enclosing box |
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| 428 | int dim, // dimension of space |
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| 429 | int n_bnds, // number of bounds |
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| 430 | ANNorthHSArray bnds, // bounds array |
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| 431 | ANNorthRect &inner_box) // inner box (returned) |
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| 432 | { |
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| 433 | annAssignRect(dim, inner_box, bnd_box); // copy bounding box to inner |
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| 434 | |
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| 435 | for (int i = 0; i < n_bnds; i++) { |
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| 436 | bnds[i].project(inner_box.lo); // project each endpoint |
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| 437 | bnds[i].project(inner_box.hi); |
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| 438 | } |
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| 439 | } |
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